EP0497543A2 - Méthode augmentée de recherche et de gestion à liste à double chaînage pour un système ayant des données mémorisées sous forme de liste - Google Patents

Méthode augmentée de recherche et de gestion à liste à double chaînage pour un système ayant des données mémorisées sous forme de liste Download PDF

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Publication number
EP0497543A2
EP0497543A2 EP92300700A EP92300700A EP0497543A2 EP 0497543 A2 EP0497543 A2 EP 0497543A2 EP 92300700 A EP92300700 A EP 92300700A EP 92300700 A EP92300700 A EP 92300700A EP 0497543 A2 EP0497543 A2 EP 0497543A2
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European Patent Office
Prior art keywords
list
data elements
doubly
array
linked list
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Withdrawn
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EP92300700A
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German (de)
English (en)
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EP0497543A3 (en
Inventor
James Arthur Porter, Jr.
Donald E. Matthews
Dennis Eugene Haugh
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Digital Equipment Corp
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Digital Equipment Corp
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Publication of EP0497543A2 publication Critical patent/EP0497543A2/fr
Publication of EP0497543A3 publication Critical patent/EP0497543A3/en
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/90—Details of database functions independent of the retrieved data types
    • G06F16/901—Indexing; Data structures therefor; Storage structures
    • G06F16/9024—Graphs; Linked lists
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10S707/00—Data processing: database and file management or data structures
    • Y10S707/99931—Database or file accessing
    • Y10S707/99933—Query processing, i.e. searching

Definitions

  • This present invention is related to storing data on a digital computer, and in particular, to an improved method of managing and searching medium amounts of data.
  • a search method is a method that accepts an argument a and tries to find a record whose key is a .
  • the method may return the entire record or, more commonly, it may return a pointer to that record. It is possible that the search for a particular argument in a table is unsuccessful; that is, there is no record in the table with that argument as its key. In such a case, the method may return a special "nil record" or a nil pointer. Very often, if a search is unsuccessful, it may be desirable to add a new record with an argument as its key. A method that does this is called a search and insertion method. A successful search is often called a retrieval.
  • search is applicable to a table that is organized either as an array or as a linked list.
  • a sequential search method would examine each key in turn, and upon finding one that matches the search argument, its index (which as a pointer to its record) is returned. If no match is found, 0 is returned.
  • the number of comparisons depends on where the record in the argument key appears in the table. If the record is the first one in the table, only one comparison is performed; if the record is the last one in the table, n comparisons are necessary. If it is equally likely for an argument to appear at any given table position, a successful search will take (on the average) ( n +1)/2 comparisons, and an unsuccessful search will take n comparisons. In any case, the number of comparisons is O(n), that is, a function of n , the size of the table or list.
  • the most efficient method of searching a sequential list without the use of auxiliary indices or lists is a binary search.
  • the problem is trivial. Otherwise, compare the item being searched for with the item at the middle of the array (or list). If they are equal, the search has been completed successfully. If the middle element is greater than the item being searched for, the search process is repeated in the first half of the array (since if the item appears anywhere, it must appear in the first half); otherwise, the process is repeated in the second half. Note that each time a comparison is made, the number of elements yet to be searched is cut in half.
  • this method is superior to the sequential search, in which each comparison reduces the number of elements yet to be searched by only one.
  • Each comparison in a binary search reduces the number of possible candidates by a factor of 2.
  • the maximum number of key comparisons that will be made is approximately log(2) n .
  • the binary search method can only be used if the list is stored as an array. This is because it makes use of the fact that the indices of array elements are consecutive integers. For this reason, in the past, the binary search has been found to be useless in situations where there are many insertions or deletions, so that an array structure is inappropriate.
  • Additional methods for searching and managing lists of elements include 3-2 tree searching methods, B-tree of order m searching methods, Balanced Binary Tree searching methods, and various other methods that are typically found in college level data structures text books, such as A. Tenenbaum & M.Augenstein, Data Structures Using Pascal (Prentice-Hall 1981).
  • a 3-2 tree is one which each node has two or three sons and contains either one or two keys. If a node has two sons, it contains one key. All keys in its left subtree are less than that key and all keys in its right subtree are greater than that key. If a node has three sons, it contains two keys. All keys in its left subtree are less than its left key, which is less than all keys in its middle subtree. All keys in its middle subtree are less than its right key, which is less than all keys in its right subtree.
  • a B-tree of order m is a generalization of the 3-2 trees.
  • Such a tree is defined as a general tree that satisfies the following properties:
  • a Balanced Binary Tree is a binary tree in which the heights of the two subtrees of every node never differ by more than one.
  • the balance of a node in a binary tree is defined as the height of its left subtree minus the height of its right subtree. Node deletion is not covered within the Balanced Binary Tree method, and must be done using other techniques.
  • a detailed treatment of Balanced Binary Trees may be found in any of several college-level textbooks on data structures, as mentioned previously.
  • the Balanced Binary Tree techniques while academically elegant, may be viewed as being more complex and may incur much more compute overhead for tree node deletions.
  • cached controllers are expected to be dynamically deleting as well as adding cache index entries to their cache data structures. This extra overhead needed for deletions (a non-deterministic amount of processing requirements) does not fair well in a storage controller with real-time constraints.
  • An array is created in memory and initialized to contain no components.
  • a group of ordered elements is set up using a doubly-linked list.
  • the doubly-linked list is grouped into list segments.
  • the address component of the initial member of each list segment is placed in the array.
  • the relationship between the number of data elements and the corresponding number of list segments with their corresponding address components is dynamic in that the groupings of list segments may change in response to the addition or deletion of data elements.
  • Search time is minimized in that in looking for any one data element, the number of steps required in sequentially searching the data element list is reduced to beginning at the first component of a list segment. Initiating a search involves a binary search on the array of address components, and then entry into the doubly-linked list at the start of the corresponding list segment. Additional objects and advantages of the invention will become clear from the following description.
  • the present invention provides a system having data stored in a list of ordered data elements in memory, a method of searching and maintaining the data in memory comprising the steps of:
  • the step of dynamically grouping the ordered data elements in the doubly-linked list into list segments includes the steps of:
  • the present invention further provides a system having data stored in a list of ordered data elements in memory, a method of searching and maintaining the data in memory comprising the steps of:
  • the step of dynamically realigning the number of ordered data elements within a list segment may include the steps of:
  • step of dynamically realigning the number of data elements within a list segment may include the steps of:
  • the present invention further provides a system having data stored in a list of ordered data elements in memory, a method of searching and maintaining the data in memory comprising the steps of:
  • the invention has characteristics of arrays and doubly-linked lists. Since it is a doubly-linked list augmented with an array, the technique of this invention has been termed Augmented Doubly-Linked list, or ADL list.
  • the augmented doubly-linked list ( ADL list ) search and management method comprises an array of address components 10 providing a plurality of entry points 14 into a doubly-linked list of data elements 12.
  • the doubly-linked list of data elements 12 is divided into a plurality of list segments 16 . Any number of data elements 17 can be associated with address components 18 , as will be described below beginning with Fig. 3 . Furthermore, it is shown below that several dynamic events occur during the addition or deletion of a data element 17. As the number of data elements 17 change in the doubly-linked list 12 , the number of list segments 16 may change. If there is a change in the number data elements within the list segments 16 , then the address components 18 will change in response, thereby changing the entry points 14 that are required to access the first data element of each list segment 16.
  • a linked list is the simplest type of dynamic data structure. It provides a solution to the problem of maintaining a list to which components may be added or deleted at random.
  • a list that has backward as well as forward pointers is called a doubly-linked list 18 . It makes additions and deletions efficiently, but it is time consuming if the entire list needs to be traversed in order to effect a change in the total number of data elements.
  • Linked structures like the doubly-linked list 12 , usually have several pointers associated with them. These pointers act as place markers, maintaining contact with the beginning of a list, its end, the current position, etc.
  • Fig. 2 is a flow diagram illustrating the manner in which a typical search of the ADL list is accomplished.
  • a search is initiated 20 and a binary search 22 is applied to the array of address components 18 .
  • the search is narrowed down to one list segment 16 of the doubly-linked list so that overall seek time is dramatically reduced by eliminating the need to search the entire doubly-linked list.
  • the appropriate list segment 16 may then be linearly traversed 24 to determine if the desired data element 17 is present or not. If the desired data element is not found 30 a new data element will be added to the list 32 . If the desired data element is found 26 the search is complete 28.
  • Fig. 3 specifically represents five data elements 17 , 17a, 17b, 17c, 17d in the doubly-linked list of data elements 12 associated with two address components 18 and 18a in the array of address components 10.
  • a search for data element 17d would begin by executing a binary search on the array of address components 10 to identify the address component 18a .
  • Address component 18a would provide the entry point 14a into the list segment 16a , specifically into data element 17b .
  • Linear traversal of the list segment 16a would begin from data element 17b , through data element 17c , until the desired list element 17d was encountered.
  • Fig. 3 represents a snapshot of the ever changing ADL list structure.
  • the ADL list structure changes in response; a change in the total number of data elements 17 produces a potential change in the number of list segments 16 , the number of data elements in any given list segment, and a corresponding change in the number of address components 18 in the ordered array 10 .
  • Fig. 3 illustrates how the ADL list accomplishes both the binary searching of an array and the minimization of sequential searching on a doubly-linked list by having only the address component of the first data element of each list segment placed in the ordered array 10 . More specifically in Fig. 3 , the address component 18 in the ordered array 10 provides entry into the first data element 17 of list segment 16 , and the address component 18a in the ordered array 10 provides entry into the first data element 17b of list segment 16a .
  • Fig. 4 is a flow diagram illustrating the manner in which the ADL list manages that data element list to minimize seek time of any one data element.
  • data elements need to be dynamically added to the list 48 and data elements need to be dynamically deleted or removed from the list 46.
  • the integer value of the total number of data elements is determined 44 .
  • This value 44 which is a whole number, is compared with the current number of doubly-linked list segments that are present, identified as check threshold alignment 50 , to determine whether a new dynamic regrouping needs to be applied 54 or not 52 . Ideal balancing occurs when the total number of data elements are associated into equal groupings.
  • FIG. 5 An example of how the addition of data elements affects the dynamic groupings of list segments in the ADL list can be viewed in following the changes in the overall ADL list structure in Figs. 5, 6, 7, 8, 9, and 10 .
  • Fig. 5 four data elements 17, 17a, 17b, 17c are grouped into two list segments 16 and 16a .
  • the array of address components 10 is populated with two address components 18 and 18a , providing two list entry points 14 and 14a into list data elements 17 and 17b , the initial members of list segments 16a and 16a , respectively.
  • the integer value of the square root of the number of data elements, in this case, four data elements, is again 2. This provides the number of array elements, i.e. address components 18 , necessary to correspond to the required number of list segments 16 .
  • List segment 16 contains data elements 17 and 17a .
  • List segment 16a contains data elements 17b and 17c .
  • Fig. 6 includes five data elements 17, 17a, 17b, 17c, 17d, grouped into two list segments 16 and 16a .
  • the array 10 of address components is populated with two address components 18 and 18a , providing two list entry points 14 and 14a into list data elements 17 and 17b , the initial members of list segments 16 and 16a , respectively.
  • the integer value of the square root of the number of data elements, in this case, five data elements, is still 2. This provides the number of array elements necessary to correspond to the required number of list segments.
  • List segment 16 contains data elements 17 and 17a.
  • List segment 16a contains data elements 17b , 17c and 17d , resulting in a slight imbalance.
  • Fig. 7 includes six data elements 17, 17a, 17b, 17c, 17d, 17e, equally grouped into two list segments 16 and 16a .
  • the array of address components 10 is populated with two address components 18 and 18a , providing two list entry points 14 and 14a into list data elements 17 and 17c , the initial members of list segments 16 and 16a , respectively.
  • the integer value of the square root of the number of data elements, in this case, six data elements, is 2. This provides the number of array elements necessary to correspond to the required number of list segments.
  • List segment 16 contains data elements 17, 17a and 17b.
  • List segment 16a contains data elements 17c, 17d and 17e.
  • Fig. 8 includes seven data elements 17, 17a, 17b, 17c, 17d, 17e, 17f , grouped into two list segments 16 and 16a , again, slightly imbalanced.
  • the array of address components 10 is populated with two address components 18 and 18a , providing two list entry points 14 and 14a into list data elements 17 and 17c , the initial members of list segments 16 and 16a , respectively.
  • the integer value of the square root of the number of data elements, in this case, seven data elements, remains at 2. This provides the number of array elements necessary to correspond to the required number of list segments.
  • List segment 16 contains data elements 17, 17a and 17b .
  • List segment 16a contains data elements 17c, 17d, 17e and 17f .
  • Fig. 9 includes eight data elements 17, 17a, 17b, 17c, 17d, 17e, 17f, 17g , grouped into two equal list segments 16 and 16a .
  • the array of address components 10 is populated with two address components 18 and 18a , providing two list entry points 14 and 14a into list data elements 17 and 17d, the initial members of list segments 16 and 16a , respectively.
  • List segment 16 contains data elements 17, 17a, 17b and 17c.
  • List segment 16a contains data elements 17d, 17e, 17f and 17g .
  • Fig. 10 includes a gross restructuring of nine data elements 17 , 17a, 17b, 17c, 17d, 17e, 17f, 17g, 17h , which are now grouped into three list segments 16, 16a and 16c .
  • the array of address components 10 is populated with three address components 18, 18a and 18b , providing three list entry points 14, 14a and 14b into list data elements 17, 17c and 17f , the initial members of list segments 16, 16a and 16c , respectively.
  • the integer value of the square root of the number of data elements, in this case, nine data elements, has now changed to 3.
  • List segment 16 contains data elements 17, 17a and 17b .
  • List segment 16a contains data elements 17c , 17d and 17e .
  • List segment 16b contains data elements 17f , 17g and 17h .
  • Fig. 11 shows how the next level of gross restructuring occurs at integer value 5, this being at the point when twenty-five data elements are in the doubly-linked list 12 . More particularly, Fig. 11 shows twenty-five data elements 17, 17a, 17b, 17c, 17d, 17e, 17t, 17g, 17h, 17i, 17j, 17k, 17l, 17m, 17n, 17o, 17p, 17q, 17r, 17s, 17t, 17u, 17v, 17w and 17x , grouped into five list segments 16, 16a, 16b, 16c, and 16d .
  • the array of address components 10 is filled with five address components 18, 18a, 18b, 18c and 18d, providing five list entry points 14, 14a, 14b, 14c and 14d into list data elements 17, 17e, 17j, 17o and 17t .
  • List segment 16 contains data elements 17, 17a, 17b, 17c and 17d .
  • List segment 16a contains data elements 17e, 17f, 17g, 17h and 17i .
  • List segment 16b contains data elements 17j, 17k, 17l, 17m and 17n .
  • List segment 16c contains data elements 17o, 17p, 17q, 17r and 17s .
  • List segment 16d contains data elements 17t, 17u, 17v, 17w and 17x .
  • Fig. 12 shows the dynamic relationship between the total number of data elements (horizontal scale 60 ) and the corresponding number of list segments (vertical scale 62 ). More, specifically, the step type graph 64 shows how the ADL list structure changes in response to the addition or deletion of data elements in the doubly-linked list, resulting in a dynamic grouping of the structure to minimize search time.
  • a doubly-linked list of data elements is grouped into smaller list segments by using a simple mathematical relationship. Entry into each list segment is provided by associating an array of address components as a means to access each list segment directly. Search time is minimized by first performing a binary search on the address component array, and only then performing a sequential search of the data elements in the doubly-linked list.
  • the number of list segments and corresponding number od address components in the array is mathematically related to the total number of data elements, and dynamically changes as data elements are added or deleted from the list, with a realignment of the number of data elements in each individual list segment until there is a change in the integer value.

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EP9292300700A 1991-01-31 1992-01-28 Augmented doubly-linked list search and management method for a system having stored listed data elements Withdrawn EP0497543A3 (en)

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US648079 1984-09-07
US07/648,079 US5263160A (en) 1991-01-31 1991-01-31 Augmented doubly-linked list search and management method for a system having data stored in a list of data elements in memory

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EP0497543A3 EP0497543A3 (en) 1994-09-14

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EP0497543A3 (en) 1994-09-14
US5263160A (en) 1993-11-16
CA2060335A1 (fr) 1992-08-01

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